Brachylog, 4 4 3 bytes
ġ=∋₁ġ=Ṁ
Explanation
ġ=∋₁ġ=Ṁ Implicit input, say "abcabc"
ġ Split into chunks of equal lengths (except maybe the last one): ["abc","abc"]
= Constrain Apply the chunksconstraint tothat beall of the chunks are equal.,
∋₁Ṁ Get the secondand chunk,that makingthere sureare itmultiple exists:of "abc"them.
The program prints true.
if the constraints can be satisfied, and false.
if not.